We consider the acoustic flow field of rotationally symmetric systems, like an annular combustor and in a round duct, absence mean azimuthal field. focus on instabilities, which manifest as either spinning (rotating) waves or standing waves, linear combination two. These instabilities are often excited by some level background noise that makes system randomly change between states, undergo ampl...

The use of averaging has long been known to reduce noise in statistically independent systems that exhibit similar levels stochastic fluctuation. This concept is general and applies a wide variety physical man-made phenomena such as particle motion, shot noise, atomic clock stability, measurement uncertainty reduction, methods signal processing. Despite its prevalence for reducing statistical u...